查询词典 Green theorem

Based on the Betti-Rayleigh dynamic reciprocal theorem, the reciprocal property of the Green function is demonstrated; and the analytical solution of soil vibration subjected to moving loads is deduced. By means of double Fourier integral transform, the problem is firstly transformed into wave number-frequency domain, which makes it very convenient to derive the solution and furthermore to analyze the frequency characteristics of soil vibration.

基于Betti-Rayleigh动力互易定理，论证了地基土Green函数的互易性，推导了移动荷载引起的地基土振动解析解，进而推证出移动常力荷载和移动简谐荷载作用下地基于表面振动在波数－频率域内和空间－时间域内的解析表达式，并采用Matlab对其进行数值计算。

Based on the fundamental theory of impulsive differential systems, employing Green formula, Gauss divergence theorem, Jensen inequality and Gronwall-Bellman inequality with impulse, we discuss the oscillation of impulsive partial differential systems by adopting reduction to absurdity and the stability in via of comparison theorem, respectively. Especially, we take an in-depth study on the oscillation of neutral impulsive parabolic systems and the stability of a class of nonlinear impulsive partial differential equations and obtain some useful conclusions.

本学位论文以脉冲微分系统基本理论为基础，利用反证法的分析方法和比较定理，结合Green公式、Gauss散度定理、Jensen不等式、含脉冲的Gronwall-Bellman不等式以及相关数学工具研究了脉冲偏微分系统的振动理论和稳定性理论，特别对中立型脉冲时滞抛物系统的振动性和一类非线性脉冲偏微分系统的稳定性作了较为深入的研究，给出了一些有用的结论。

Consequently, Divergence theorem, Green's theorem and Stokes' theorem those very important and active applications in applied engineering are our main goals of this course.

譬如说，Divergence Theorem、Green's Theorem、Stokes' Theorem等，这些在物理学、流体力学、应用力学以及电磁场学上被广泛应用的重要定理。

Key words : seepage force; boundary water pressure; Green theorem; piping; slope sliding; critical gradient

关键 词：渗透力；边界水压力；格林公式；管涌；滑坡；临界坡降

Employing the GREEN theorem, the boundary integral equations for solving the ground surface potential are derived for the first time, both for one object underground and for complicated geological structure.

利用格林公式首次推导出了单一目标体和复杂地质结构两种情况下直流电阻率正演模拟中求解表面电位的边界积分方程。

In Chapter 3, we consider the semi-direct product AG, and analyze the decomposition in AG of idempotents of AH, and obtain a precise algebraic description; as a corollary, we show a criterion of the primitivity in AG of a primitive idempotent of AH, hence a theorem of Fong and a theorem of Green are generalized to an uniform setting.

考虑半直积AG，我们分析了AH的幂等元在AG中的分解模式，得到了一个准确的代数刻画；作为它的推论，给出了AH的本原幂等元在AG中仍然本原的判断准则，从而将Fong的定理和Green的定理推广到了一个统一的情形。

Part Ⅰ deals with the foundmental theory of variational technique in the lossy electromagnetic fields. In chapter two and three the Green theorem is introduced so the unified method to derive functional is given. Chapter four is devoted to discuss two type of inner product. In chapter five the generialized least function theorem is given and applied in the derivation of variational expressions.

第一篇主要是关于有耗电磁变分的基础理论，由四章组成，前二章引入了以Green定理为核心的边值问题理论，建立了电磁变分的普遍理论，第四章从对称的观点出发讨论了建立泛函的两种内积形式，第五章给出了一般电磁场的广义最小作用量原理，并用之解决变分问题。

In this paper the conflicting discussion of scholastic view-point on seepage force which has lasted many years is stated. Then the physical concept of seepage force and its related forces including the resolved two components (a seepage force and a buoyant force) from seepage resultant force, the transformation between the seepage force and boundary pore water pressures, schematic diagram of forces acting on unit soil mass and the mathematic proof by Green theorem are described.

追述了多年来对渗透力学术观点的争论，并再就此问题论述了渗透力的物理概念及其与之相关的各力（包括渗流作用合力及其分解成的两个分力，渗透力与周边孔隙水压力的转换关系及各力作用在单位土体的图示；从数学上引用格林公式，证明土体表面水压力与土体本身渗透力之间的转换关系。

Moreover,we also gave the proofs of generalization formula of integration by parts,the Green s formula of first type and the Green s formula of second type by using the divergence theorem .

首先指出数学分析中反映二重积分和第二类平面线积分联系的Green公式可以看成是散度定理的一种特殊情形，然后利用散度定理给出广义分部积分公式、第一Green公式和第二Green公式的证明

Difference equations; Green's function; Fixed point theorem; Fixed point index; Positive solutions; Cone

基础科学，数学，数学分析差分方程； Green函数；不动点定理；不动点指数；正解；锥

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。